.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 1607x_1^4+6895x_1^3x_2-10246x_1^2x_2^2+5569x_1x_2^3+2680x_2^4+6813x_1^
------------------------------------------------------------------------
3x_3+3785x_1^2x_2x_3+8646x_1x_2^2x_3+1239x_2^3x_3-11272x_1^2x_3^2+10892x
------------------------------------------------------------------------
_1x_2x_3^2-13855x_2^2x_3^2-8142x_1x_3^3+10203x_2x_3^3+1902x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-14406x_1x_3^2+11382x_2x_3^2+1777x_3^3
------------------------------------------------------------------------
x_1x_2x_3+1839x_1x_3^2+769x_2x_3^2+11128x_3^3
------------------------------------------------------------------------
x_1^2x_3-5695x_1x_3^2+5709x_2x_3^2+3876x_3^3
------------------------------------------------------------------------
x_2^3+8565x_1x_3^2+14302x_2x_3^2-6792x_3^3
------------------------------------------------------------------------
x_1x_2^2-14848x_1x_3^2-10750x_2x_3^2-11451x_3^3
------------------------------------------------------------------------
x_1^2x_2+5751x_1x_3^2-2337x_2x_3^2+6227x_3^3
------------------------------------------------------------------------
x_1^3-12969x_1x_3^2+6964x_2x_3^2+10955x_3^3 |
1 7
o3 : Matrix R <--- R
|
i4 : res ideal f
1 7 7 1
o4 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o4 : ChainComplex
|
i5 : betti oo
0 1 2 3
o5 = total: 1 7 7 1
0: 1 . . .
1: . . . .
2: . 7 7 .
3: . . . .
4: . . . 1
o5 : BettiTally
|